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Fig. 27.7. Contribution of each term to the total control action. Proportional action gets small as the error disappears. Integral action takes on large values even when the error is zero. Derivative action only appears when the system is moving

For proportional control (P control), the Z-N rules suggest that Kc = Kcu/2 = 0.21 and the simulation results of this tuning are shown in Fig. 27.9; here is infinite and rd is zero.

The controller performance shown in the graph can be improved. On the one hand, the measured variable does not reach the new set point; this difference in the steady state is called offset. On the other hand, the manipulated variable moves too strongly, which can be deleterious to the actuator or to the process. As seen in Fig 27.10, other Kc values can be tried to improve this performance.

Here we see that, with proportional control alone, we cannot reduce the offset and smooth the control action at the same time. If we reduce the proportional gain, a smooth control action is achieved, but the offset increases. On the contrary, a larger gain reduces the offset but at the expense of an oscillating control action.

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